Information processing apparatus and GPS positioning method

ABSTRACT

A composite integrated semiconductor device. In one embodiment, an input surge/noise absorbing circuit absorbs surge from an input signal, an attenuating/level-shifting circuit attenuates or level-shifts the input signal, and an electrical signal converting circuit converts the input signal to an output signal. The input surge/noise absorbing circuit, the attenuating or level-shifting circuit, and the electrical signal converting circuit together form a unit, and a plurality of these units are arranged in parallel in one semiconductor substrate to form the composite integrated semiconductor device, resulting in a reduction in the number of discrete components mounted on a printed circuit board.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.11/275,963, filed Feb. 7, 2006, now allowed, which is a continuationapplication of International PCT Application No. PCT/JP2003/010352,which was filed on Aug. 14, 2003, the contents of which are incorporatedby reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an information processing apparatus andGPS positioning method for measuring a position by utilizing the Dopplereffect of a GPS (global positioning system) satellite.

2. Description of the Related Art

GPS positioning techniques utilizing a satellite (i.e., GPS satellite)are currently taken advantage of by diverse categories of informationprocessing apparatuses such as a vehicle mounted apparatus, a mobileinformation terminal (e.g., personal digital assistant: PDA), a mobilephone, a PHS (Personal Handyphone System) and a PC (personal computer).

GPS positioning can largely be categorized into stand alone positioningand interference positioning. The former is a method for acquiring noless than four GPS satellites, measuring pseudo-distances from ameasuring point to the respective satellites, solving simultaneousequations containing four unknowns, and thereby calculating the positionof the measuring point. Whereas the latter is a method for positioningby using a plurality of measuring points utilizing wave interference.The present invention relates to the former method, i.e., the standalone positioning.

Navigation data of each GPS satellite used for GPS positioning is mainlycategorized into almanac data and ephemeris data. The almanac datadescribes parameters for figuring out approximate positions of all theGPS satellites and can be used for about two weeks. The time limit isgoverned by the orbits of the respective GPS satellites changing withtime and corresponds to the expiration date of the data.

The ephemeris data describes detailed parameters of satellite orbitalinformation about each satellite and is used by an informationprocessing apparatus for calculating the position of each satellite. Thetime limit of the ephemeris data is about two hours.

FIG. 1 is an operation flow chart of a conventional stand alonepositioning. First, an information processing apparatus receives a radiowave in a radio frequency (RF) band from a GPS satellite and converts itinto a signal in an intermediate frequency (IF) band by down conversion(step 101).

Then it searches for a receiving frequency of the radio wave from theGPS satellite (step 102), in which information from a target satelliteis extracted by multiplying a signal of the receiving radio wave by theCA code (coarse acquisition code) of the target satellite whileconsidering the Doppler effect.

It then receives an almanac and ephemeris data from the target satellite(step 103). Likewise it receives navigation data from other GPSsatellites. Recent times have seen systems for complementing theinformation by receiving the navigation data by way of another wirelessnetwork.

Then it calculates the pseudo-distance to each satellite from a radiowave emission clock time and radio wave receiving clock time for eachsatellite (step 104) and calculates the position of the measuring pointby using the navigation data and the pseudo-distance of each satellite(step 105).

The equation used for the calculation in the step 105 is the following,defining the position of the measuring point by the coordinates (x, y,z), and the positions of acquired i-th GPS satellites by the coordinates(x_(i), y_(i), z_(i)) for instance:√{square root over ((x−x ₁)²+(y−y _(i))²+(z−z _(i))²)}+C _(b) =R _(i)  (1)where C_(b) expresses an amount caused by the clock difference betweenthe satellite and the information processing apparatus, and R_(i)expresses the pseudo-distance between the i-th satellite and themeasuring point. The coordinates (x_(i), y_(i), z_(i)) can be figuredout from the ephemeris data of the respective satellites. Therefore, asolution is obtainable with the number of acquired satellites becomingno less than four because there are four unknowns in the equation, i.e.,x, y, z and C_(b). If a measuring point is restricted to the surface ofthe earth, a solution is obtainable with the number of acquiredsatellite being three.

As described above, the stand alone positioning generally requires theacquisition of four GPS satellites, but it is difficult to acquire foursatellites simultaneously in a metropolis such as Tokyo, Japan, withmany skyscrapers (i.e., super tall buildings) towering in places.

Let the case of measuring point moving from point A to point B on a roadsurrounded by a cluster of skyscrapers 201 through 206 as exemplified byFIG. 2 be considered. In this case, the number of acquired satellites isconsidered to increase at the points A and B since the four directionsare visible, while the number of acquired satellites will be limited tothe direction the same as the line connecting the points A and B duringthe time of moving from the point A to point B since the clusters ofskyscrapers 202 and 205 are in the way. This prevents acquisition of thenecessary number of satellites, resulting in an incapability ofpositioning.

In order to solve this problem, a car navigation system, et cetera,carries out complementary processing by an integrated use of techniquessuch as a gyro sensor, gradient sensor, vehicle speed sensor, mapmatching. Such techniques, however, are not yet practical whenconsidering application to a mobile terminal represented by a mobilephone or a PHS.

Accordingly, a reduced number of GPS satellites required for positioningis desired for locations such as streets in the midst of skyscrapers.The use of the Doppler effect associated with the movement of satellitescan be considered as such a method for reducing the number of acquiredsatellites.

There is a known technique for approximating a current position based onreceived signals from two satellites through the use of the Dopplereffect (e.g., refer to patent document 1 below). The method disclosedthereby, however, is not capable of positioning a measuring pointaccurately.

Patent document 1 :Japan patent application publication No. 2000-235067

SUMMARY OF THE INVENTION

An object of the present invention is to provide an informationprocessing apparatus and GPS positioning method capable of obtaining theposition of a measuring point with high precision by using a receivedsignal from a small number of GPS satellites (N.B.: sometimes simply“satellite” herein).

An information processing apparatus according to the present invention,comprising a Doppler shift measurement unit, a distance measurementunit, a data acquisition unit and an arithmetic calculation unit, isconfigured to measure a current position by using a radio wave from aGPS satellite.

In a first positioning method, the Doppler shift measurement unitobtains the Doppler shift in the frequency of the radio wave from thesatellite; and the distance measurement unit obtains the pseudo-distancebetween the satellite and a measuring point by using a signal from thesatellite. The data acquisition unit acquires navigation data of thesatellite. The arithmetic calculation unit obtains the position of thesatellite and the relative velocity between the measuring point and thesatellite from the navigation data, and calculates the position of themeasuring point by using the obtained information, i.e., the positionand the relative velocity of the satellite, the Doppler shift and thepseudo-distance.

The first positioning method makes it possible to obtain the position ofa measuring point with high precision if the clock of the satellite isaccurately synchronous with that of the information processingapparatus.

In a second positioning method, the Doppler shift measurement unitobtains the Doppler shift in the frequency of a radio wave from a firstsatellite and that in the frequency of a radio wave from a secondsatellite. The distance measurement unit obtains the pseudo-distancebetween the first satellite and a measuring point by using a signal fromthe first satellite, and that between the second satellite and themeasuring point by using a signal from the second satellite. The dataacquisition unit acquires respective navigation data of the first andsecond satellites.

The arithmetic calculation unit obtains the position of the firstsatellite and the relative velocity of the measuring point with respectto the first satellite from the navigation data thereof; and theposition of the second satellite and the relative velocity between themeasuring point and the second satellite from the navigation datathereof. And the arithmetic calculation unit calculates the position ofthe measuring point by using the obtained information, i.e., theposition and relative velocity of the first satellite, the position andrelative velocity of the second satellite, the Doppler shift of theradio wave from the first satellite, that of the radio wave from thesecond satellite, the pseudo-distance between the first satellite andthe measuring point, and that between the second satellite and themeasuring point.

The second positioning method makes it possible to obtain the positionof a measuring point with high precision even if the clock of thesatellite is not synchronous with that of the information processingapparatus.

The Doppler shift measurement unit corresponds to a later describedcorrelator 604 or Doppler shift measurement module 609, both shown byFIG. 6 for example; and the distance measurement unit, data acquisitionunit and arithmetic calculation unit correspond to a distancemeasurement module 605, navigation data analysis module 606 andarithmetic calculation circuit 607, respectively shown by FIG. 6.

The present invention enables the position of a measuring point to beaccurately calculated by using only one GPS satellite under goodconditions or only two thereof under normal conditions.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an operation flow chart of conventional stand alonepositioning;

FIG. 2 shows measuring points in a street of skyscrapers;

FIG. 3 shows a conical surface where the same Doppler shift as ameasuring point is observed;

FIG. 4 describes a Lorentz transformation effect;

FIG. 5 describes a Galilean transformation effect;

FIG. 6 shows a configuration of an information processing apparatus;

FIG. 7 shows a configuration of an arithmetic calculation circuit;

FIG. 8 is an operation flow chart of stand alone positioning accordingto the present invention;

FIG. 9 shows positions of two measuring points corresponding to thetheoretical maximum value and minimum value of Doppler shiftrespectively; and

FIG. 10 shows two line segments corresponding to Doppler shift error oftwo satellites respectively.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The following is a detailed description of the preferred embodiment ofthe present invention referring to the accompanying drawings.

As described above, the conventional stand alone positioning measuresthe pseudo-distance between a GPS satellite and a measuring point tocalculate the position of the measuring point. This is a method forobtaining the position of the measuring point from satellite positionsat a positioning instance.

Each satellite moves along a determined orbit at a determined velocity.This movement brings forth a Doppler effect and therefore it isnecessary to match a receiving frequency with a frequency shifted by anamount corresponding to the Doppler effect in order for an informationprocessing apparatus to receive information from the satellite. As amethod for measuring the Doppler shift, the information processingapparatus checks a correlation value between a signal from the satelliteand a CA code generated by the information processing apparatus per seand locks the receiving frequency when detecting a correlation value ofa prescribed threshold value or greater.

That is, the information processing apparatus detects a Doppler shift ofthe satellite. This Doppler shift is the apparent Doppler shift alongthe line of sight from a measuring point 302 on the earth 301 to atarget satellite 303 as shown by FIG. 3.

In FIG. 3, the satellite 303 is moving along the orbit 304 at a velocityvector 305 so that the apparent Doppler shift occurs in response to anapparent velocity vector 306 along the line of sight at the measuringpoint 302. The same Doppler shift can be observed at an arbitrary pointon a conical surface 307 which is drawn by rotating the velocity vector306 around the velocity vector 305 as the central axis. If the distancebetween the satellite and the measuring point is known in addition tothe Doppler shift, then the position of the measuring point canapparently be calculated.

The next description is of a positioning algorithm according to thepresent embodiment. First, there are two contributing factors to achange in the frequency of a radio wave due to the Doppler effect:

-   -   (1) the Lorentz transformation effect, and    -   (2) the Galilean transformation effect,    -   where general relativistic effects are ignored herein.

As shown by FIG. 4, a change in frequency due to a Lorentztransformation effect occurs if a GPS satellite 402 is movingperpendicular to the line of sight of an observer 401, that is, even atan instant when the distance between the observer 401 and the satellite402 is not changing. This is a special relativistic effect.

Letting a cycle time in an inherent time of the observer 401 beT_(lorentz), a cycle time of a radio wave in an inherent time of thesatellite be T₀, a velocity of the observer 401 (i.e., relativevelocity) looking from the satellite 402 be V and the velocity of lightbe c, the relationship between T_(lorentz) and T₀ is expressed accordingto the Lorentz transformation as follows: $\begin{matrix}{T_{lorentz} = \frac{T_{0}}{\sqrt{1 - \frac{V^{2}}{c^{2}}}}} & (2)\end{matrix}$

Therefore, a frequency ω_(lorentz) when looking from the observer 401,letting a frequency of the satellite be ω₀, is expressed as follows:$\begin{matrix}{\omega_{lorentz} = {\omega_{0}\sqrt{1 - \frac{V^{2}}{c^{2}}}}} & (3)\end{matrix}$

Such a compression of radio wave is called a Lorentz contraction.

As shown by FIG. 5, an effect of Galilean transformation is caused by achanging distance between the observer 401 and GPS satellite 402, whichis the same as that of the Doppler effect on sound. Letting a positionalvector of the observer 401 looking from the satellite 402 be (x, y, z),the distance between the satellite 402 and observer 401 be L and avelocity vector of the observer 401 looking from the satellite 402 be(u, v, w), then a rate of change of the distance V₁ is expressed asfollows: $\begin{matrix}{V_{1} = {{\frac{\mathbb{d}\quad}{\mathbb{d}t}\sqrt{x^{2} + y^{2} + z^{2}}} = {\frac{{xu} + {yv} + {zw}}{\sqrt{x^{2} + y^{2} + z^{2}}} = \frac{{xu} + {yv} + {zw}}{L}}}} & (4)\end{matrix}$

And taking both the Lorentz transformation and Galilean transformationeffects into consideration, a cycle time T in the inherent time of theobserver 401, increasing in proportion with a positional change rate, isexpressed as follows: $\begin{matrix}{T = {\frac{V_{1}T_{lorentz}}{c} + T_{lorentz}}} & (5)\end{matrix}$

Substituting the expressions (2) and (4) into the expression (5) thefollowing expression is obtained: $\begin{matrix}{T = \frac{T_{0}( {1 + \frac{{xu} + {yv} + {zw}}{cL}} )}{\sqrt{1 - \frac{V^{2}}{c^{2}}}}} & (6)\end{matrix}$

Therefore, a frequency w when looking from the observer 401 is expressedby: $\begin{matrix}{\omega = {\omega_{0}\frac{\sqrt{1 - \frac{V^{2}}{c^{2}}}}{( {1 + \frac{{xu} + {yv} + {zw}}{cL}} )}}} & (7)\end{matrix}$

A conversion of the expression (7) results in the following:$\begin{matrix}{{{xu} + {yv} + {zw}} = {{cL}( {{\frac{\omega_{0}}{\omega}\sqrt{1 - \frac{V^{2}}{c^{2}}}} - 1} )}} & (8)\end{matrix}$

Ignoring special relativistic effects in the expression (8) thefollowing expression is obtained: $\begin{matrix}{{{{xu} + {yv} + {zw}} = {{{cL}( {\frac{\omega_{0}}{\omega} - 1} )} = {{cL}\quad\frac{\Delta\quad\omega}{\omega}}}};} & (9)\end{matrix}$where Δω represents a frequency change which is given by the followingexpression:Δω=ω₀−ω  (10)

The equation (9) expresses a curved surface in a three dimensionalspace, which the conical surface 307 shown by FIG. 3 corresponds to.Furthermore, the distance L between the satellite 402 and observer 401is expressed by:x ² +y ² +z ² =L ²   (11)

The above equation (11) expresses a spherical surface which is a curvedsurface in a three dimensional space.

If there is no clock error in the information processing apparatus usedby the observer 401, the distance L will be calculated accurately fromthe difference between a radio wave emitted clock time of the satellite402 and radio wave receiving clock time. The observer 401 stands on theline of the intersection of the conical surface expressed by theequation (9) and the spherical surface expressed by the equation (11).And adding a condition of being on the surface of the earth, thesolution usually converges to two points. Those two solution pointspresent themselves at the axisymmetric points straddling the satelliteorbit. If the measuring point were nearby and right below the satelliteorbit, the two solution points would be close to each other, but usuallyone solution actually exists in a remote location.

Therefore, it is possible to narrow down the result to one solutionpoint by filtering the two solution points by software filtering throughthe use of global positional information such as the measuring pointbeing in Japan for instance, et cetera. Needless to say, there will beone solution if a measuring point is right below the satellite orbit.

As described above, a use of the positioning algorithm according to thepresent embodiment enables a calculation of the position of a measuringpoint by using a received wave from one satellite in a certaincondition. A summary of the above described algorithm is as follows.

-   -   (a) The case of considering special relativistic effects        $\begin{matrix}        {{{( {x - x_{1}} )u_{1}} + {( {y - y_{1}} )v_{1}} + {( {z - z_{1}} )w_{1}}} = {{cL}_{1}( {{\frac{\omega_{0}}{\omega}\sqrt{1 - \frac{V^{2}}{c^{2}}}} - 1} )}} & (12) \\        {{( {x - x_{1}} )^{2} + ( {y - y_{1}} )^{2} + ( {z - z_{1}} )^{2}} = L_{1}^{2}} & (13) \\        {\sqrt{( {x - x_{E}} )^{2} + ( {y - y_{E}} )^{2} + ( {z - z_{E}} )^{2}} = R_{E}} & (14)        \end{matrix}$        where (x, y, z) is the position of the measuring point, (x₁, y₁,        z₁) is the position of satellites 402, (x_(E), y_(E), z_(E)) is        the center of the earth, R_(E) is the radius of the earth, L₁ is        a distance between the measuring point and the satellite 402,        and (u₁, v₁, w₁) is a velocity of the observer 401 looking from        the satellite 402.

In this case, solving the equations (12), (13) and (14) about (x, y, z),being quadratic equations, obtains two sets of solution. Then, one ofthem is selected by using already known global positional informationabout the measuring point.

-   -   (b) the case of ignoring special relativistic effects        $\begin{matrix}        {{{( {x - x_{1}} )u_{1}} + {( {y - y_{1}} )v_{1}} + {( {z - z_{1}} )w_{1}}} = {{cL}_{1}( \frac{\Delta\quad\omega}{\omega} )}} & (15) \\        {{( {x - x_{1}} )^{2} + ( {y - y_{1}} )^{2} + ( {z - z_{1}} )^{2}} = L_{1}^{2}} & (16) \\        {\sqrt{( {x - x_{E}} )^{2} + ( {y - y_{E}} )^{2} + ( {z - z_{E}} )^{2}} = R_{E}} & (17)        \end{matrix}$        where Δω is expressed by the equation (10).

In this case, solving the equations (15), (16) and (17) about (x, y, z)obtains two sets of solution as with the above described case (a). Then,one of them is selected by using the global positional information.

The following description is of an information processing apparatususing a positioning algorithm in the case of ignoring the abovedescribed specific relativistic effect for the sake of simplicity.

FIG. 6 shows a configuration of an information processing apparatusaccording to the present embodiment. The information processingapparatus shown by FIG. 6 comprises an antenna 601, an RF down converter(RFDC) unit 602, an analog/digital (AD) converter 603, a correlator 604,a distance measurement module 605, a navigation data analysis module606, an arithmetic calculation circuit 607 and a display unit 608.

In the case of software executing a calculation of the above describedpositioning algorithm, the arithmetic calculation circuit 607 isconfigured by using a computer which includes a CPU (central processingunit) 701 and memory 702 as shown by FIG. 7. The memory 702, includingROM (read only memory) and RAM (random access memory), stores a programand data necessary for processing. The memory 702 stores the centerposition (x_(E), y_(E), z_(E)) and radius R_(E) of the earth, afrequency ω₀ of a GPS satellite and the value of the velocity of light cas known data in advance.

Incidentally the program and data necessary for the processing can beinstalled into the information processing apparatus by way of acomputer-readable storage medium such as a memory card, flexible disk,CD-ROM (compact disk read only memory), optical disk, magneto-opticaldisk.

Alternatively, the information processing apparatus can also be enabledto download a program and data from an external apparatus (e.g., server)by way of a wireless network, et cetera. In such a case, the externalapparatus generates a propagation signal for propagating the program anddata and transmits it to the information processing apparatus by way ofa transmission medium on the wireless network.

FIG. 8 is an operation flow chart of stand alone positioning carried outby the information processing apparatus shown by FIG. 6. First of all,the antenna 601 receives a radio wave from a GPS satellite, and the RFDCunit 602 converts the received wave into a signal of the IF band (step801).

Then, the A/D converter 603 converts the signal output from the RFDCunit 602 into a digital signal, and the correlator 604 searches for areceived frequency based on the obtained digital signal (step 802).

In this event, the correlator 604 calculates a Doppler shift amount Δωand a code shift amount by multiplying the digital signal output fromthe A/D converter 603 by the CA code of the target satellite, andoutputs the Δω to the arithmetic calculation circuit 607 and the codeshift amount to the distance measurement module 605.

Then, the information processing apparatus receives navigation data fromthe target satellite, and the navigation data analysis module 606extracts navigation data from the output of the correlator 604 to outputto the arithmetic calculation circuit 607 (step 803).

The distance measurement module 605 calculates the pseudo-distancebetween the measuring point and target satellite from the code shiftamount to output to the arithmetic calculation circuit 607 (step 804).If a clock difference between the target satellite and informationprocessing apparatus is small enough, the pseudo-distance can be used asthe distance L₁ between the measuring point and target satellite.

The arithmetic calculation circuit 607 calculates a parameter of theconical surface by using the Δω and navigation data (step 805), byobtaining the position (x₁, y₁, z₁) of the target satellite and therelative velocity (u₁, v₁, w₁) of the measuring point with respect tothe target satellite, and obtaining w from the Δω and ω₀ to calculate aconstant term and the unknowns x, y and z of the equation (15) (step805).

Then, it solves the equations (15), (16) and (17) about (x, y, z) byusing a pseudo-distance as L₁ to calculate the position of the measuringpoint (step 806). Here, if two sets of solution are obtained, they willbe narrowed down to one by using a software filter (i.e., globalpositional information). The display unit 608 displays the calculatedpositional information as a positioning result on the display screen.

The configuration shown by FIG. 6 calculates the position of a measuringpoint by using navigation data received from the target satellite, it ispossible, however, to obtain navigation data of the target satellitefrom a server installed on a network.

Meanwhile, a Doppler shift amount Δω may be measured by a specificallyinstalled Doppler shift measurement module 609 instead of measuring Δωby the correlator 604, in which case the Doppler shift measurementmodule 609 obtains Δω from the output signal of the A/D converter 603 tooutput to the arithmetic calculation circuit 607.

Note that the above described algorithm premises an accuratesynchronization of clocks between a satellite and an informationprocessing apparatus. Such a premise usually becomes effective rightafter the stand alone positioning is carried out once by a certainmethod, but is not available at an initial positioning. Consequently, itis necessary to carry out positioning by using a plurality of GPSsatellites if those clocks in the satellite and information processingapparatus are not synchronous with each other. Accordingly, the nextdescription is of a positioning algorithm for such a case.

A use of two GPS satellites obtains two sets of the equations (15) and(16), two sets of equation (1) expressing a clock time difference, andfurther the equation (17) exists as a constraining condition, makingseven equations to be solved as follows: $\begin{matrix}{{{( {x - x_{1}} )u_{1}} + {( {y - y_{1}} )v_{1}} + {( {z - z_{1}} )w_{1}}} = {c\quad L_{1}\frac{\Delta\quad\omega_{1}}{\omega_{1}}}} & (18) \\{{{( {x - x_{2}} )u_{2}} + {( {y - y_{2}} )v_{2}} + {( {z - z_{2}} )w_{2}}} = {c\quad L_{2}\frac{\Delta\quad\omega_{2}}{\omega_{2}}}} & (19) \\{{( {x - x_{1}} )^{2} + ( {y - y_{1}} )^{2} + ( {z - z_{1}} )^{2}} = L_{1}^{2}} & (20) \\{{( {x - x_{2}} )^{2} + ( {y - y_{2}} )^{2} + ( {z - z_{2}} )^{2}} = L_{2}^{2}} & (21) \\{{\sqrt{( {x - x_{1}} )^{2} + ( {y - y_{1}} )^{2} + ( {z - z_{1}} )^{2}} + {c\quad\Delta\quad T}} = R_{1}} & (22) \\{{\sqrt{( {x - x_{2}} )^{2} + ( {y - y_{2}} )^{2} + ( {z - z_{2}} )^{2}} + {c\quad\Delta\quad T}} = R_{2}} & (23) \\{{\sqrt{( {x - x_{E}} )^{2} + ( {y - y_{E}} )^{2} + ( {z - z_{E}} )^{2}} = R_{E}};} & (24)\end{matrix}$where, the following lists the definition of each parameter:

-   -   (x₁, y₁, z₁): position of first satellite;    -   (u₁, v₁, w₁): relative velocity of a measuring point with        respect to the first satellite;    -   L₁: distance between the measuring point and first satellite;    -   R₁: pseudo-distance between the measuring point and first        satellite;    -   Δω₁: Doppler shift amount of the first satellite;    -   ω₁: apparent frequency of the first satellite;    -   (x₂, Y₂, z₂): position of a second satellite;    -   (u₂, v₂, w₂): relative velocity of the measuring point with        respect to the second satellite;    -   L₂: distance between the measuring point and second satellite;    -   R₂: pseudo-distance between the measuring point and second        satellite;    -   Δω₂: Doppler shift amount of the second satellite;    -   ω₂: apparent frequency of the second satellite; and    -   ΔT: clock time difference (common to the two satellites).

Since the relationship between the distance L_(i) and pseudo-distanceR_(i) is expressed by L_(i)=R_(i)−cΔT, the equations (20) and (21) aredependent on each other, and so are the equations (21) and (23).Accordingly, elimination of two of the interdependent equations willleave five equations to be solved. On the other hand, there are fourunknowns, i.e., position of measuring point (x, y, z) and clock timedifference ΔT, resulting in one excess equation. A utilization of thisredundancy enables a reduction of positioning error.

Here, error mixing, variable quantities are limited to Δω_(i). As Δω_(i)fluctuates, the calculated position of a measuring point walks on anapproximately straight line on the surface of the earth as shown by FIG.9, forming a line segment representing a positioning identificationerror. Actually, this position walks on a circular arc, but it can beregarded as an approximate straight line because the radius of the earthis very large.

In FIG. 9, a satellite 901 is moving along the satellite orbit accordingto a velocity vector 902, and a line segment on the earth surface 907 isparallel with the velocity direction of the satellite. The position (x,y, z) of the starting point 906 of the line segment is calculated fromthe conical surface 904 of the Doppler effect corresponding thetheoretical minimum value of Δω_(i), and the position (x, y, z) of theterminal point 905 is calculated from the conical surface 903corresponding to the theoretical maximum value of Δω_(i).

The theoretical maximum and minimum values of Δω_(i) express the upperand lower limit values of the Doppler shift amount estimated from ameasurement result. For example, if the minimum unit of measurement ofΔω_(i) is 1 Hz and a measurement result is 1234 Hz, then the theoreticalmaximum value is 1235 Hz and the theoretical minimum value 1233 Hz.

Here, if two line segments 1001 and 1002 respectively obtained bymeasurement results by using two satellites intersect as shown by FIG.10, the position of the point of intersection 1003 is regarded as theclosest to the true position. Therefore the adoption of this position asthe position of the measuring point makes positioning error extremelysmall, theoretically positioning error caused by Δω_(i) approaches zero.However errors caused by other factors are not taken into consideration.

The basic operation in the case of using such a positioning algorithm isthe same as FIG. 8, except that the operations of the steps 801 through804 will be carried out for the two satellites respectively. Then in thesteps 805 and 806 the arithmetic calculation circuit 607 carries out theprocesses of:

-   -   (1 -1) calculating (x, y, z) and ΔT by using the theoretical        maximum value of Δω₁ and the equations (18), (22), (23) and        (24);    -   (1-2) calculating (x, y, z) and ΔT by using the theoretical        minimum value of Δω₁ and the equations (18), (22), (23) and        (24);    -   (1-3) calculating (x, y, z) and ΔT by using the theoretical        maximum value of Δω₂ and the equations (19), (22), (23) and        (24);    -   (1 -4) calculating (x, y, z) and ΔT by using the theoretical        minimum value of Δω₂ and the equations (19), (22), (23) and        (24);    -   (1-5) obtaining an equation for a first straight line connecting        a point calculated from the theoretical maximum value of Δω₁ and        a point calculated from the theoretical minimum value thereof;    -   (1-6) obtaining an equation for a second straight line        connecting a point calculated from the theoretical maximum value        of Δω₂ and a point calculated from the theoretical minimum value        thereof; and    -   (1-7) obtaining the intersection point between the first and        second straight lines and confirming that the obtained        intersection point is on the two line segments as follows:    -   a line segment connecting a point calculated from the        theoretical maximum value of Δω₁ and a point calculated from the        theoretical minimum value thereof; and    -   a line segment connecting a point calculated from the        theoretical maximum value of Δω₂ and a point calculated from the        theoretical minimum value thereof.

If the intersection point is not on either line segment, the abovedescribed processes (1-1) through (1-7) will be repeated by increasingthe minimum unit of measurement of Δω_(i) by a prescribed value. Andwhen obtaining an intersection point between the two line segments, theposition of the intersection point will be output as the position of themeasuring point.

Such a positioning algorithm enables a calculation of the position ofthe measuring point by using respectively received waves from two GPSsatellites only, if the clocks of the satellites and informationprocessing apparatus are not synchronous with each other. Moreover, ifthe clock of the information processing apparatus is synchronized withthat of the satellite by using the simultaneously obtained ΔT, standalone positioning by using one satellite is maintained effective for aperiod of time thereafter.

The same positioning algorithm can be used for the case of acquiring onesatellite after a time lag, for a stationary measuring point, instead ofacquiring two satellites. In such a case, the information processingapparatus acquires the same satellite again in a certain period of timeafter acquiring it for the first time, regards the satellite acquiredfor the first time as the first satellite and the satellite acquired forthe second time as the second satellite to carry out a positioning bythe processes of:

-   -   (2-1) acquiring a target satellite to perform the processes of        the above described (1-1) and (1-2) by regarding the acquired        satellite as the first satellite;    -   (2-2) acquiring the same satellite anew after a certain period        of time to perform the processes of the above described (1-3)        and (1-4) by regarding the acquired satellite as the second        satellite; and    -   (2-3) performing the processes of the above described (1-5)        through (1-7). The processing in the case of the intersection        point not being on either line segment is the same as described        above.

While the above described embodiment deals with the positioning methodby using either one or two GPS satellites, the number of satellites isin no way limited to either one or two, and rather, larger numbers ofsatellites may be used for further improving positioning accuracy.

1. An information processing apparatus for measuring a current positionby using a radio wave from a single GPS satellite, comprising: a Dopplershift measurement unit obtaining a Doppler shift in a frequency of theradio wave from the satellite; a distance measurement unit obtaining apseudo-distance between the satellite and a measuring point by using asignal from the satellite; and an arithmetic calculation unitcalculating a position of the measuring point by using the Doppler shiftcombined with the pseudo-distance, thereby obtaining the position of themeasuring point with high precision using only the single GPS satellitewhen a clock of the satellite is synchronous with a clock of theinformation processing apparatus.
 2. The information processingapparatus according to claim 1, further comprising a data acquisitionunit acquiring navigation data of the satellite, wherein said arithmeticcalculation unit obtains a position of the satellite and a relativevelocity between the measuring point and the satellite from thenavigation data, and calculates the position of the measuring point byusing the obtained position and relative velocity of the satellite, theDoppler shift and the pseudo-distance.
 3. The information processingapparatus according to claim 2, wherein said arithmetic calculation unitcalculates the position of said measuring point by using an algorithmderived from a Lorentz transformation effect and a Galileantransformation effect including calculations of: a conical surface wherethe same Doppler shift as said measuring point is observed; a sphericalsurface whose radius equals a distance between the satellite and themeasuring point; and an earth surface.
 4. The information processingapparatus according to claim 3, wherein said arithmetic calculation unitobtains two positions of said measuring point by using the algorithmderived from the Lorentz transformation effect and the Galileantransformation effect, and selects one of the two positions by usingglobal positional information of the measuring point.
 5. The informationprocessing apparatus according to claim 2, wherein said arithmeticcalculation unit calculates the position of said measuring point byusing said pseudo-distance as an actual distance between said satelliteand the measuring point after a clock of the satellite synchronizes witha clock of said information processing apparatus.
 6. A storage mediumstoring a program for use in an information processing apparatus formeasuring a current position by using a radio wave from a single GPSsatellite, wherein the program enables the information processingapparatus to perform: obtaining a Doppler shift in a frequency of theradio wave from the satellite; obtaining a pseudo-distance between thesatellite and a measuring point by using a signal from the satellite;and calculating a position of the measuring point by using the Dopplershift combined with the pseudo-distance, thereby obtaining the positionof the measuring point with high precision using only the single GPSsatellite when a clock of the satellite is synchronous with a clock ofthe information processing apparatus.
 7. The storage medium according toclaim 6, wherein said program further enables said informationprocessing apparatus to perform obtaining navigation data of thesatellite, wherein said calculating obtains a position of the satelliteand a relative velocity between the measuring point and the satellitefrom the navigation data, and calculates the position of the measuringpoint by using the obtained position and relative velocity of thesatellite, the Doppler shift and the pseudo-distance.
 8. The storagemedium according to claim 7, wherein said information processingapparatus calculates the position of said measuring point by using analgorithm derived from a Lorentz transformation effect and a Galileantransformation effect including calculations of: a conical surface wherethe same Doppler shift as said measuring point is observed; a sphericalsurface whose radius equals a distance between the satellite and themeasuring point; and an earth surface.
 9. The storage medium accordingto claim 8, wherein said information processing apparatus obtains twopositions of said measuring point by using the algorithm derived fromthe Lorentz transformation effect and the Galilean transformationeffect, and selects one of the two positions by using global positionalinformation of the measuring point.
 10. The storage medium according toclaim 7, wherein said information processing apparatus calculates theposition of said measuring point by using said pseudo-distance as anactual distance between said satellite and the measuring point after aclock of the satellite synchronizes with a clock of said informationprocessing apparatus.
 11. An information processing apparatus formeasuring a current position by using a radio wave from a GPS satellite,comprising: a Doppler shift measurement unit obtaining a Doppler shiftin a frequency of the radio wave from the satellite; a distancemeasurement unit obtaining a pseudo-distance between the satellite and ameasuring point by using a signal from the satellite; an arithmeticcalculation unit calculating a position of the measuring point by usingthe Doppler shift combined with the pseudo-distance; and a dataacquisition unit acquiring navigation data of the satellite, whereinsaid arithmetic calculation unit obtains a position of the satellite anda relative velocity between the measuring point and the satellite fromthe navigation data, and calculates the position of the measuring pointby using the obtained position and relative velocity of the satellite,the Doppler shift and the pseudo-distance, and wherein said arithmeticcalculation unit calculates the position of said measuring point byusing an algorithm derived from a Lorentz transformation effect and aGalilean transformation effect including calculations of: a conicalsurface where the same Doppler shift as said measuring point isobserved; a spherical surface whose radius equals a distance between thesatellite and the measuring point; and an earth surface.
 12. Theinformation processing apparatus according to claim 11, wherein saidarithmetic calculation unit obtains two positions of said measuringpoint by using the algorithm derived from the Lorentz transformationeffect and the Galilean transformation effect, and selects one of thetwo positions by using global positional information of the measuringpoint.
 13. A storage medium storing a program for use in an informationprocessing apparatus for measuring a current position by using a radiowave from a GPS satellite, wherein the program enables the informationprocessing apparatus to perform: obtaining a Doppler shift in afrequency of the radio wave from the satellite; obtaining apseudo-distance between the satellite and a measuring point by using asignal from the satellite; calculating a position of the measuring pointby using the Doppler shift combined with the pseudo-distance; andobtaining navigation data of the satellite, wherein said calculatingobtains a position of the satellite and a relative velocity between themeasuring point and the satellite from the navigation data, andcalculates the position of the measuring point by using the obtainedposition and relative velocity of the satellite, the Doppler shift andthe pseudo-distance, and wherein said information processing apparatuscalculates the position of said measuring point by using an algorithmderived from a Lorentz transformation effect and a Galileantransformation effect including calculations of: a conical surface wherethe same Doppler shift as said measuring point is observed; a sphericalsurface whose radius equals a distance between the satellite and themeasuring point; and an earth surface.
 14. The storage medium accordingto claim 13, wherein said information processing apparatus obtains twopositions of said measuring point by using the algorithm derived fromthe Lorentz transformation effect and the Galilean transformationeffect, and selects one of the two positions by using global positionalinformation of the measuring point.